continuum mechanics

Conventional constitutive modeling heavily relies on expert knowledge and suffers from low automation. Method: This paper proposes a large language model (LLM)-driven, end-to-end framework for constitutive modeling. It is the first approach enabling an LLM to autonomously design physics-constrained neural networks (CANNs) tailored for solid mechanics—automatically embedding physical laws, generating network architectures, and producing executable code based solely on input material type and experimental data. The framework tightly integrates domain knowledge with data-driven learning, eliminating manual architecture design and hard-coded physical constraints. Contribution/Results: Evaluated on multiple benchmark problems, the automatically generated models achieve accuracy comparable to or exceeding that of handcrafted models, while demonstrating superior extrapolation capability and generalization across diverse loading conditions.

Addressing the challenge of a priori selecting appropriate strain invariants and determining the functional form of strain energy in hyperelastic constitutive modeling, this paper proposes a data-driven framework that unifies generalized invariant discovery with constitutive relation learning within a single neural network architecture. The framework jointly learns both the optimal combination of strain invariants and the corresponding nonlinear strain energy mapping directly from experimental data. Designed for isotropic, incompressible materials, it balances physical interpretability with high predictive accuracy. Validation on rubber and brain tissue datasets demonstrates that the method automatically recovers classical stretch-dominated models (e.g., Neo-Hookean, Mooney–Rivlin) and accurately captures the nonlinear shear response of brain tissue under small deformations. Quantitatively, it achieves significantly higher prediction accuracy than conventional phenomenological models and state-of-the-art neural network-based approaches.

This work proposes a purely physics-driven deep energy method to address the computational expense and need for repeated training inherent in conventional approaches when dealing with continuously stochastic material parameters in solid mechanics. By embedding both spatial coordinates and random constitutive parameters into the neural network input, the method enables zero-shot, real-time prediction of displacement fields for arbitrary unseen material parameter realizations through unsupervised minimization of the expected potential energy over the parameter space. This framework establishes, for the first time, a unified modeling paradigm that requires neither training datasets nor retraining, demonstrating consistent efficacy across elastic, hyperelastic, and nonlinear contact mechanics problems while significantly outperforming traditional finite element methods and data-driven surrogate models.

This work addresses the challenge of high-fidelity, efficient simulation of dynamic behaviors of real-world elastic objects. Methodologically, we propose a continuum-mechanics-based neural simulation framework that employs Gaussian kernels as fundamental continuous material units and introduces a Center-of-Mass System (CMS) hierarchical architecture—explicitly embedding physical constraints such as mass and momentum conservation to enable interpretable, physics-consistent modeling across coarse-to-fine granularities. Our key contributions are: (i) the first integration of Gaussian kernels into continuum-based elastic modeling, and (ii) the introduction of an explicit physics-constrained CMS hierarchical simulation paradigm. Evaluated on our newly established READY benchmark—a real-world video dataset—the method significantly outperforms existing physics-driven approaches in dynamic simulation accuracy. Both source code and trained models will be made publicly available.

This work addresses nonlinear large-deformation elastodynamic systems. We propose the first structure-preserving discrete modeling and numerical method grounded in the port-Hamiltonian (pH) framework. Leveraging variational principles, we derive index-1 differential-algebraic equations and perform index reduction to construct a complete pH state-space model—featuring displacement, velocity, and **nonlinear strain as an independent state variable (novel in pH modeling)**—rigorously preserving passivity, losslessness, and angular momentum conservation. We further design a structure-preserving midpoint-type discrete-gradient time-integration scheme. Numerical experiments demonstrate exact long-term conservation of energy and angular momentum, significantly enhancing physical fidelity and numerical robustness. The method establishes a provably structure-stable paradigm for high-fidelity dynamic simulation of hyperelastic bodies.

This study addresses the challenge of accurately capturing the highly nonlinear response of hyperelastic materials under large-deformation impact, which traditional constitutive models struggle to represent. The authors integrate physics-augmented neural networks (PANNs) into industrial-scale explicit finite element solvers—Simcenter Radioss and OpenRadioss—by automatically generating Fortran user material subroutines for data-driven constitutive modeling. Key contributions include the first deployment of PANNs within industrial explicit solvers, the introduction of a computationally more efficient SQuarePlus activation function as a replacement for SoftPlus, and an open-source, automated toolchain enabling end-to-end subroutine generation. Experimental results demonstrate that the proposed approach achieves high accuracy while significantly reducing neural network evaluation overhead, offering an efficient and practical machine learning–based constitutive modeling paradigm for impact simulations.

Traditional simulation of deformable objects relies on mesh-based representations or neural fields requiring per-shape optimization, struggling to balance geometric complexity and computational efficiency. This work proposes a mesh-free reduced-order simulation method that, for the first time, integrates Reproducing Kernel Particle Method (RKPM) with reduced-order elastic dynamics. By employing RKPM to construct a continuous elastic body model and solving the generalized eigenvalue problem of the elastic energy Hessian matrix, the method automatically computes skinning weights without mesh generation or per-shape optimization. The approach achieves a 40× speedup in training compared to neural field–based methods, yields simulation errors lower than those of converged finite element solutions, and demonstrates successful application across diverse geometric representations and robotic simulation tasks.

This work addresses the high computational cost of traditional numerical homogenization methods in predicting the effective mechanical properties of hyperelastic composites with Boolean microstructures. A supervised learning–based neural network surrogate model is proposed, integrating multiscale statistical descriptors—including area fraction, shape descriptor τ, two-point correlation function S₂(r), and lineal path function ℓ(z)—to enable rapid prediction of effective Lamé parameters for two-phase hyperelastic composites. Model extrapolation capability is enhanced through data augmentation with extreme loading scenarios, and generalization performance is rigorously evaluated via leave-one-grain-type-out cross-validation. The study demonstrates that combining τ and S₂(r) suffices for accurate and compact modeling, while inclusion of ℓ(z) further reduces sampling error, albeit requiring careful attention to physical plausibility within interpolation regions.

This study addresses the challenge of achieving efficient and highly accurate model order reduction for large-deformation solid mechanics problems involving parametrized materials and boundary conditions. It extends strain-space hyper-reduction methods—specifically ECM, E3C, and EMSL—to non-uniform large-deformation scenarios for the first time. By constructing, offline, compatible lifting fields that satisfy arbitrary Dirichlet boundary conditions, the approach rigorously enforces boundary consistency. In two hyperelastic test cases, the proposed strain-space methods significantly outperform the displacement-space ECSW method: EMSL achieves acceleration of approximately 10⁵-fold, while E3C delivers exceptional accuracy at only marginally higher computational cost. This work overcomes key limitations of conventional displacement-based reduced-order modeling in nonlinear large-deformation settings.

Traditional constitutive modeling struggles to integrate multimodal, multifidelity experimental data and faces a trade-off between physical consistency and discovery efficiency. This work proposes paFEMU, a novel framework that, for the first time, combines sparse regression–driven constitutive discovery with finite element model updating. By leveraging only a few simple mechanical tests and full-field digital image correlation (DIC) data, the method employs physics-informed neural networks and adjoint-based optimization to efficiently identify interpretable constitutive relationships. The resulting models are low-dimensional, physically consistent, and amenable to transfer learning across materials. Moreover, they can be seamlessly integrated into existing finite element simulation workflows, offering a practical pathway toward data-driven, yet physically grounded, material modeling.